IFRS 4 slides appendix E time value of money

Financial Accounting
IFRS 4th Edition
Appendix E
Time Value of Money
Weygandt ● Kimmel ● Kieso

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Copyright ©2019 John Wiley & Son, Inc.
Appendix Preview
Would you rather receive NT$1,000 today or a year from
now?
You should prefer to receive the NT$1,000 today because
you can invest the NT$1,000 and earn interest on it. As a
result, you will have more than NT$1,000 a year from
now. What this example illustrates is the concept of the
time value of money. Everyone prefers to receive money
today rather than in the future because of the interest
factor.

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Appendix Outline

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Copyright ©2019 John Wiley & Sons, Inc.
Learning Objective 1
Compute interest and future values.
LO 1

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Nature of Interest
• Payment for the use of money.
• Difference between the amount borrowed or
invested (principal) and the amount repaid or
collected.
• Three elements determine the amount of interest:
1. Principal (p): The original amount borrowed or invested.
2. Interest Rate (i): Annual percentage of the principal.
3. Time (n): The number of periods that the principal is borrowed or
invested.
LO 1

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Nature of Interest
Simple Interest
Interest is computed on the principal (p) only.
Assume: You borrowed NT$5,000 for 2 years at a simple interest rate of
6% annually.
Calculate: Annual interest.
LO 1

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Nature of Interest
Compound Interest
• Computes interest on
• the principal and
• any interest earned that has not been paid or
withdrawn.
• Business situations use compound interest when
interest is not paid periodically during the time of
borrowing.
LO 1

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Compound Interest
Assume: You deposit €1,000 in Bank Two, where it will earn simple
interest of 9% per year, and you deposit another €1,000 in Citizens
Bank, where it will earn compound interest of 9% per year
compounded annually. Also assume that in both cases you will not
withdraw any cash until three years from the date of deposit.
LO 1

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Future Value Concepts
LO 1
Future value of a single amount
• Value at a future date of a given amount invested, assuming compound
interest
FV = future value of a single amount
p = principal (or present value; the value today)
i = interest rate for one period
n = number of periods

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Future Value Concepts
LO 1
• Value at a future date of a given amount invested, assuming
compound interest
FV = future value of a single amount
p = principal (or present value; the value today)

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LO 1
Assume: You deposit €1,000 for three years. The annual interest
rate is 9%.
Calculate: The future value after three years.
FV = p × (1 + i)n
= €1,000 × (1 + .09)3
= €1,000 × 1.29503
= €1,295.03

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LO 1
Assume: Again, you deposit €1,000 for three years. The annual
interest rate is 9%.
Calculate: The future value after three years using a table.
What factor do we use?
Present Value x Factor = Future Value
€1,000 x 1.29503 = €1,295.03

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LO 1
Assume: John and Mary Rich invested £20,000 in a savings account
paying 6% interest at the time their son, Mike, was born. The money is
to be used by Mike for his college education. On his 18th birthday, Mike
withdraws the money from his savings account.
Calculate: How much did Mike withdraw from his account?
Which table do we use?

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LO 1
Present Value x Factor = Future Value
£20,000 x 2.85434 = £57,086.80
… … … … … … … … … …

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LO 1
Future value of an annuity
Assume: You invest HK$2,000 at the end of each year for three
years at 5% interest compounded annually.
Calculate: The future value after three years using a table.
Continues on next slide
When the periodic payments (or receipts) are the same in each period, the
future value can be computed by using a Future Value of an Annuity of 1 table
(Table 2).

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LO 1

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LO 1
Assume: John and Char Lewis’ daughter, Debra, has just started high
school. They decide to start a college fund for her and will invest £2,500
in a savings account at the end of each year she is in high school (4
payments total). The account will earn 6% interest compounded
annually.
Calculate: How much will be in the college fund at the time Debra
graduates from high school?

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LO 1
Payment x Factor = Future Value
£2,500 x 4.37462 = £10.936.55

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Compute present values.
LO 2

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Present Value Concepts
Present value of a single amount
The present value is the value now of a given amount to
be paid or received in the future, assuming compound
interest.
Present value variables:
1. Future Value (FV): Dollar amount to be received
2. Interest Rate (i): Called the discount rate
3. Time (n): length of time until amount is received (number of periods).
LO 2

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LO 2
Present value of a single amount:
Value now of a given future amount invested, assuming compound interest.
PV = present value
FV = the dollar amount to be received in the future

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LO 2
Assume: You make a deposit and want a 10% rate of return. The
future value of the deposit in one year is €1,000.
Calculate: The present value.
PV = FV ÷ (1 + i)n
= €1,000 ÷ (1 + .10)1
= €1,000 ÷ 1.10
= €909.09

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LO 2
Assume: Again, you make a deposit and want a 10% rate of
return. The future value of the deposit in one year is €1,000.
Calculate: The present value using a table.
Future Value x Factor = Present Value
€1,000 x 0.90909 = €909.09

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LO 2
Assume: You make a deposit and want a 10% rate of return. The
future value of the deposit in two years is €1,000.
PV = FV ÷ (1 + i)n
= €1,000 ÷ (1 + .10)2
= €1,000 ÷ 1.10
= €826.45

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LO 2
Assume: Again, you make a deposit and want a 10% rate of
return. The future value of the deposit in two years is €1,000.
Calculate: The present value using a table.
€1,000 x 0.82645 = €826.45

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LO 2
Assume: You have a winning lottery ticket. You have the option of
taking NT$100,000 three years from now or taking the present value of
NT$100,000 now. The discount rate is 8%.
Calculate: How much will you receive if you accept your winnings now?
NT$100,000 x 0.79383 = NT$79,383

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LO 2
Assume: You want to accumulate £5,000 for a down payment on a
new car 4 years from now.
Calculate: How much do you have to deposit today in your super
savings account, paying 9% interest?
£5,000 x 0.70843 = £3,542.15

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Present value of an annuity
The present value is the value now of a series of amounts to be
paid or received in the future, assuming compound interest.
Present value variables:
1. Interest Rate (i): Called the discount rate
2. Number of payments (n): the number of payments (receipts)
3. Payment: the amount of the periodic payments (receipts)
LO 2

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LO 2
Assume: You will receive €1,000 cash annually for three years at a
time when the discount rate is 10%.
Calculate: The present value in this situation.

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LO 2
Assume: You will receive €1,000 cash annually for three years at a
time when the discount rate is 10%.
Calculate: The present value in this situation using a table.
Future Amount x Factor = Present Value
€1,000 x 2.48685 = €2,486.85

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LO 2
Assume: Kildare Construction has just signed a finance lease contract for
equipment that requires rental payments of €6,000 each, to be paid at the end
of each of the next 5 years. The appropriate discount rate is 12%.
Calculate: What is the present value of the rental payments—that is, the
amount used to finance the leased equipment?
€6,000 x 3.60478 = €21,628.68

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LO 2
Time periods and discounting
When the time frame is less than one year, it is necessary to convert the annual
interest rate to the applicable time frame.
Assume: An investor received €500 semiannually for three years instead of
€1,000 annually. The annual discount rate is 10%.
Calculate: The present value in this situation using a table.

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Time periods and discounting
Comparing compounding results:
Two €500 payments per year -> PV = €2,537.85
One €1,000 payment per year -> PV = €2,486.86
The higher number of payments results in a higher present value.
LO 2
€500 x 5.07569 = €2,537.85

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LO 2
Present value of a long-term note or bond
Assume: An issue of 10%, five-year bonds with a face value of
NT$100,000 with interest payable semiannually on January 1 and
July 1. The bonds sell at face value.
Calculate: The present value of the principal and interest payments.

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LO 2
Continues on next
slide

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LO 2

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LO 2
Calculate: The present value of the principal and interest payments
when the investor’s required rate of return is 12%, not 10%.
We expect a lower present value.
Continues on next
slide

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LO 2

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LO 2
We expect a higher present value.
Continues on next
slide

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LO2

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Use a financial calculator to solve time
value of money problems.
LO 3

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LO 3
Time value of money
with a financial calculator
N = Number or periods
I = Interest rate per period (I or i/y on the calculator)
PV = Present value
PMT = Payment
FV = Future value

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LO 3
Assume: You want to know the present value of €84,253 to be
received in five years, discounted at 11% compounded annually.

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LO 3
Assume: You are asked to determine the present value of rental
receipts of €6,000 each to be received at the end of each of the
next five years, when discounted at 12%.

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LO 3
Useful applications: Auto loan
Assume: You are financing the purchase of a used car with a
three-year loan. The loan has a 9.5% stated annual interest rate,
compounded monthly. The price of the car is €6,000.
Calculate: The monthly payments, assuming that the payments
start one month after the purchase.

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LO 3
Useful applications: Mortgage loan
• Assume: You are evaluating financing options for a loan on a
house (a mortgage). You decide that the maximum mortgage
payment you can afford is €700 per month. The annual interest
rate is 8.4%.
Calculate: If you get a mortgage that requires you to make
monthly payments over a 15- year period, what is the maximum
home loan you can afford?

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IFRS 4 slides appendix E time value of money

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